Question: Simplify the following expression: $\sqrt{175} + \sqrt{112}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{175} + \sqrt{112}$ $= \sqrt{25 \cdot 7} + \sqrt{16 \cdot 7}$ Separate the radicals and simplify. $= \sqrt{25} \cdot \sqrt{7} + \sqrt{16} \cdot \sqrt{7}$ $= 5\sqrt{7} + 4\sqrt{7}$ Finally, simplify by combining the terms. $= ( 5 + 4 )\sqrt{7} = 9\sqrt{7}$